This invention relates generally to magnetic resonance imaging, and more particularly the invention relates to the correction of gradient spatial encoding waveforms due to gradient system inaccuracy, magnetic field inhomogeneity, and eddy currents.
Magnetic resonance imaging (MRI), is a non-destructive method for the analysis of materials and represents a new approach to medical imaging. It is completely non-invasive and does not involve ionizing radiation. In very general terms, nuclear magnetic moments are excited at specific spin precession frequencies which are proportional to the local magnetic field. The radio-frequency signals resulting from the precession of these spins are received using pickup coils. By manipulating the magnetic fields, an array of signals is provided representing different regions of the volume. These are combined to produce a volumetric image of the nuclear spin density of the body.
Briefly, a strong static magnetic field is employed to line up atoms whose nuclei have an odd number of protons and/or neutrons, that is, have spin angular momentum and a magnetic dipole moment. A second RF magnetic field, applied as a single pulse traverse to the first, is then used to pump energy into these nuclei, flipping them over, for example to 90.degree. or 180.degree.. After excitation, the nuclei gradually return to alignment with the static field and give up the energy in the form of weak but detectable free induction decay (FID). These FID signals are used by a computer to produce images.
The excitation frequency, and the FID frequency, is defined by the Larmor relationship which states that the angular frequency .omega..sub.0, of the procession of the nuclei is the product of the magnetic field B.sub.0, and the so-called magnetogyric ratio, .gamma., a fundamental physical constant for each nuclear species: EQU .omega..sub.0 =B.sub.0 .times..gamma.
Accordingly, by superimposing a linear gradient field, B.sub.z =Z.times.G.sub.z, on the same static uniform field, B.sub.0, which defines the Z axis, for example, nuclei in a selected X-Y plane can be excited by proper choice of the frequency spectrum of the transverse excitation field applied along the X or Y axis. Similarly, a gradient field can be applied in the X-Y plane during detection of the FID signals to spatially-localize the FID signals in the plane. The angle of nuclear spin flip in response to an RF pulse excitation is proportional to the integral of the pulse over time.
A k-space interpretation of nuclei excitation is given by Pauly, Nishimura, and Macovski in "A k-space Analysis of Small-Tip-Angle Excitation," Journal of Magnetic Resonance 81, 43-56 (1989).
Eddy currents and gradient system imperfections give rise to a time-varying error between a prescribed magnetic field and the actual magnetic field. Takahashi et al, MRM 34: 446, 1995 measure the actual field by using a self-encoding technique which uses a separate calibration sequence to measure one dimensional trajectories in k-space. Essentially, a self-encoding gradient lobe moving to k.sub.0 in k-space is applied, then data is acquired while applying the test waveform. A gradient-recalled echo occurs each time the self-encode lobe is refocussed. These echo time indicate when k.sub.0 is reached by the test waveform. In practice, multiple self encodes and acquisitions are used, with echo peak interpolation done against self-encode values to determine the actual k-space trajectory. Peak interpolation is performed by fitting a Gaussian curve using least-squares.
The present invention utilizes gradient, G(t), measurements, as described by Takahashi et al., in spin echo, echo-planar, and spiral imaging. Additionally, the actual phase of the static magnetic field, B.sub.0 (t), is determined using a self-encode method.